School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Niavaran Bldg., Niavaran Square, Tehran, P.O. Box: 19395-5746, Iran. samanehsaberali@gmail.com
In this paper, we study conformal vector fields on Finsler manifolds. Let (M,g) be an Einstein-Finsler manifold of dimension n ≥ 2. Suppose that V is conformal vector field on M. We show that V is a concircular vector field.
1. P. Agrawal, On the concircular geometry in Finsler spaces, Tensor N.S. 23(1972), 333- 336.
2. H. Akbar-Zadeh, Initiation to Global Finslerian Geometry, North-Holland Mathematical Library, 2006.
3. S. B´acs´o and X. Cheng, Finsler conformal transformations and the curvature invariants, Publ. Math. Debrecen. 70(2007), 221-231.
4. B. Bidabad and P. Joharinad, Conformal vector fields on Finsler spaces, Differ. Geom. App. 31(2013), 33–40.
5. B. Bidabad and Z. Shen, Circle-preserving transformations in Finsler spaces, Publ. Math. Debr. 81(2012), 435-445.
6. H.W. Brinkmann, Einstein spaces which are mapped conformally one achother, Math. Ann. 94(1925), 119145.
7. B.-Y. Chen, Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific Publishing, Hackensack, 2011.
8. G. Chen, X. Cheng and Y. Zou, On Canformal transformations between two (α, β) metrics, Diff. Geom. Appl. 31(2013), 300-307.
9. X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S-curvature, Israel J. Math. 169(2009), 317-340.
10. S.S. Chern and Z. Shen, Reimann-Finsler Geometry, Nankai Tracts Math, World Scientific, 2005.
11. A. Deicke, Uber die Finsler-Raume mit ¨ Ai = 0, Arch. Math. 4(1953), 45-51.
12. A. Fialkow, The conformal theory of curves. Trans. Am. Math. Society. 51(1942), 435- 497.
13. S. Ishihara, On infinitesimal concircular transformations, Kˆodai Math. Sem. Rep. 12(1960), 45-56.
14. S. Ishihara and Y. Tashiro, On Riemannian manifolds admitting a concircular transformation, Math. J. Okayama Univ. 9 (1959), 19-47.
15. W. K¨uhnel, and H-B. Rademacher, Conformal diffeomorphisms preserving the Ricci tensor, Proc. American. Math. Soc. 123(1995) , 2841–2848.
16. W. K¨uhnel, Conformal Transformations between Einstein Spaces, 1988, Volume 12.
17. M. Maleki and N. Sadeghzadeh, On conformally related spherically symmetric Finsler metrics, Int. J. Geom. Meth. Modern. Phys. 13(10) (2016), 1650118, 16 pages.
18. S. Masoumi, Projective vector fields on special (α, β)-metrics, Journal of Finsler Geometry and its Applications, 1(2) (2021), 83-93.
19. X. Mo and H. Zhu, On a class of locally projectively flat general (α, β)-metrics, Bull. Korean. Math. Soc. 54(2017), 1293-1307.
20. M. Obata, Conformal transformations of Riemannian manifolds, J. Differential Geom. 4(1970), 311-333.
21. S. F. Rutz, Symmetry in Finsler spaces, Contemporary Math. 196(1996), 289-300.
22. Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, (2001).
23. Z. Shen and G. Yang, On concircular transformations in Finsler geometry, Results. Math. 74(2019), 162.
24. Z. Shen and C. Yu, On a class of Einstein Finsler metrics, Int. J. Math. 25(04) (2014), 1450030.
25. Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. math. Soc. 117(1965), 251-275.
Saberali, S. (2021). On conformal vector fields on Einstein Finsler manifolds. Journal of Finsler Geometry and its Applications, 2(2), 114-121. doi: 10.22098/jfga.2021.1373
MLA
Samaneh Saberali. "On conformal vector fields on Einstein Finsler manifolds", Journal of Finsler Geometry and its Applications, 2, 2, 2021, 114-121. doi: 10.22098/jfga.2021.1373
HARVARD
Saberali, S. (2021). 'On conformal vector fields on Einstein Finsler manifolds', Journal of Finsler Geometry and its Applications, 2(2), pp. 114-121. doi: 10.22098/jfga.2021.1373
VANCOUVER
Saberali, S. On conformal vector fields on Einstein Finsler manifolds. Journal of Finsler Geometry and its Applications, 2021; 2(2): 114-121. doi: 10.22098/jfga.2021.1373
)